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Oct
7
comment Which is the most restrictive closed-form expression that still generates all primes?
Also note that there are expressions which generate exactly the primes. These would be the optimal solutions unless you exclude things like sums or the floor function from your notion of "closed-form expression".
Oct
7
comment Which is the most restrictive closed-form expression that still generates all primes?
The question isn't well-defined, since as you rightly point out $\sqrt{1+24n}$ doesn't generate all primes, so you'd have to say something about how many exceptions are allowed or how to combine the numbers of false positives and false negatives, e.g. look for the lowest sum of the two. Also, $\sqrt{1+24n}$ generates infinitely many non-primes, so it can't generate the smallest number of non-primes in the sense of cardinality -- are you thinking in terms of asymptotic densities?
Oct
7
revised Questions about cracking playfair using a 'shotgun climbing hill' method
that's not quite right
Oct
7
comment Questions about cracking playfair using a 'shotgun climbing hill' method
@furskytl: OK, I've added something on that to the answer.
Oct
7
revised Questions about cracking playfair using a 'shotgun climbing hill' method
response to comments
Oct
7
revised Solve the phase plane equation to obtain the integral curves for the system:
wrote out solution in response to comment
Oct
7
comment Solve the phase plane equation to obtain the integral curves for the system:
@anon: I'd written this out but then removed it because I saw the question is on homework; I'll write it out again.
Oct
7
answered Solve the phase plane equation to obtain the integral curves for the system:
Oct
7
comment Solve the phase plane equation to obtain the integral curves for the system:
The references to "him" no longer make sense after you edited out your boyfriend.
Oct
7
comment Always oddly-many ones in the binary expression for $10^{10^{n}}$?
Could you describe how you got up to $n=9$? When I take the direct approach and calculate the powers using Java's BigInteger class, already $n=7$ takes a long time; I'd presume that they use efficient methods to calculate the powers; are you doing something more sophisticated?
Oct
7
revised converting integrand limits from Cartesian to spherical
improve answer in reponse to comments
Oct
6
answered converting integrand limits from Cartesian to spherical
Oct
6
comment Residue integral problem
No special treatment is required for the cosine. You can just substitute the pole $z_0$ into $f(z)(z-z_0)$ like you would with any other function.
Oct
6
revised Name of property describing the number of times a function changes concavity?
formatting
Oct
6
comment HAKMEM 123: Fourier Clocks
In fact it doesn't, at least not for general sequences of curves. For instance, a sequence of curves that wrap $n^2$ times around concentric circles of radius $1/n$ has the constant curve at the centre as its limit, but the arc lengths diverge.
Oct
6
comment HAKMEM 123: Fourier Clocks
Rigorously speaking, how does the arc length of the partial sums going to infinity imply that the limit curve isn't rectifiable?
Oct
6
revised HAKMEM 123: Fourier Clocks
corrected sum
Oct
6
answered Questions about cracking playfair using a 'shotgun climbing hill' method
Oct
5
revised What's the distance between a ray and a sphere?
slight addendum
Oct
5
answered What's the distance between a ray and a sphere?